Add a Select field to the WordPress Customizer.

WP Customizer - Select

$wp_customize->add_setting( 'themeslug_select_setting_id', array(
  'capability' => 'edit_theme_options',
  'sanitize_callback' => 'themeslug_sanitize_select',
  'default' => 'value1',
) );

$wp_customize->add_control( 'themeslug_select_setting_id', array(
  'type' => 'select',
  'section' => 'custom_section', // Add a default or your own section
  'label' => __( 'Custom Select Option' ),
  'description' => __( 'This is a custom select option.' ),
  'choices' => array(
    'value1' => __( 'Value 1' ),
    'value2' => __( 'Value 2' ),
    'value3' => __( 'Value 3' ),
  ),
) );

function themeslug_sanitize_select( $input, $setting ) {

  // Ensure input is a slug.
  $input = sanitize_key( $input );

  // Get list of choices from the control associated with the setting.
  $choices = $setting->manager->get_control( $setting->id )->choices;

  // If the input is a valid key, return it; otherwise, return the default.
  return ( array_key_exists( $input, $choices ) ? $input : $setting->default );
}